What is 4x^2-5y^2+30y=65 ?

The solution to 4x^2-5y^2+30y=65 is Hyperbola with (h,k)=(0,3),a=sqrt(5),b=2

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4x^2-5y^2+30y=65

4 x^{2} - 5 y^{2} + 30 y = 65

(h, k) = (0, 3), a = 5, b = 2

Solution steps

4 x^{2} - 5 y^{2} + 30 y = 65

Rewrite

4 x^{2} - 5 y^{2} + 30 y = 65

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 5 ) ^{2}} - \frac{( y - 3 ) ^{2}}{2 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 3), a = 5, b = 2

4244 - 98 y + 324 x - 49 y^{2} + 81 x^{2} = 0

- 16 x^{2} + 25 y^{2} + 64 x - 100 y - 364 = 0

5 x^{2} - 10 y^{2} - 10 = 0

- 4 x^{2} + y^{2} = 4

\frac{( x - 5 ) ^{2}}{25} - \frac{( y - 5 ) ^{2}}{16} = 1

What is 4x^2-5y^2+30y=65 ?
The solution to 4x^2-5y^2+30y=65 is Hyperbola with (h,k)=(0,3),a=sqrt(5),b=2